Chapter 14Day One

Chi Square Test for Goodness of Fit

Homeworkp. 846 1,5,8

Measure the distribution of a proportions within a single population.

Goodness of Fit: does specified population distribution seem valid

Homogeneity: compare two or more population proportions

CHI SQUARE TESTS

M&Ms Advertised Color Distribtution

Brown Red Yellow Orange Blue Green

13 13 14 20 24 16

Chi-Square Table

Brown

Red Yellow Orange

Blue Green Total

ObservedExpected(O-E)2/E

Day Observed Count

Expected Count

(O-E)2/E

Sun 20Mon 133Tues 126Wed 159Thurs 136Fri 113Sat 12

Example – Chi Square Test for Goodness of Fit Are you more likely to have a motor vehicle

collision when using a cell phone? A study of 699 drivers who were suing a cell phone when they were involved in a collision examined this question. The drivers made 26,798 cell phone calls during a 14-month period. Each of 699 collisions was classified in various ways. Here are the counts for each day of the week.

Day Sun Mon Tues Wed Thurs Fri Sat TotalNumber 20 113 126 159 136 113 12 699

Ho: p Sun = pmon = pTues= ……Psat = 1/7

Ha: At least one of the proportions differs from the stated value

Calculating p-values on Chi Squared Distribution.

Example Chi Square Test for Homeogeneity of Populations Market researchers know that background music an influence

the mood and purchasing behavior of customers. One study in a supermarket in Northern Ireland compared three treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the numbers of bottles of French, Italian, and other wine purchased. Here is a table that summarizes the data.

  Populations: Population 1: bottles of wine sold while no music is playing Population 2: bottles of wine sold while French music is playing Population 3 : bottles of wine sold while Italian music is playing  

Ho: The proportions of each wine type sold are the same in all three populations

Ha: At least one proportion different

Wine/music

None French Italian Total

French 30 39 30 99Italian 11 1 19 31Other 43 35 35 113Total 84 75 84 243

Observed Data

Expected Data

Wine/music

None French Italian Total

FrenchItalianOtherTotal